1. Field of the Invention
The present invention relates to the field of “Multiple Input Multiple Output” (“MIMO”) communication systems adopting precoding techniques. More particularly, the present invention concerns a method for the selection of the optimum precoding matrix.
2. Overview of the State of the Art
Precoding is an attractive scheme that makes multiple antenna systems more robust against rank deficient channels, and provides improved performance with a limited increase in the receiver complexity.
Basically, linear precoding is realized by multiplying the layered signal (to be transmitted over a MIMO transmission channel) for a matrix, called “preceding matrix”. A “layered signal” is a signal formed by one or multiple layers that are transmitted in parallel over the radio channel through a plurality of antennas, and wherein each layer represents an independent data stream. In the following, the term “stream” is then often used as a synonym of layer.
The optimum precoding matrix is a function of the Channel State Information (CSI), which is often available only at the receiver. Thus, the information required to select the optimum precoding matrix must be fed back to the transmitter over a feedback communication link or channel, which is typically limited in terms of data rate.
The precoding matrix is chosen from a finite set of precoding matrices, said finite set being called “codebook”, known to both the receiver and the transmitter. The receiver chooses the optimal precoding matrix from the codebook as a function of the current CSI and sends a binary index of the chosen matrix to the transmitter over the feedback channel. The matrix index is denoted as Precoding Matrix Index (PMI).
Linear precoding techniques are used in recent wireless communication systems such as the LTE (Long Term Evolution) system, currently under standardization in 3GPP (Third Generation Partnership Project), and the WiMAX (Worldwide Interoperability for Microwave Access) system. For example, in case of the LTE system the linear precoding is based on a codebook and can be used both in case of single layer transmission and in case of multiple layer transmission (i.e. in case of spatial multiplexing, a transmission technique used in MIMO communication systems to transmit independent and separately encoded data signals, so-called codewords, from each of the multiple transmit antennas; the space dimension is thus reused, or multiplexed, more than one time). The term “codeword” refers to a data flow that is encoded and modulated independently under the control of the Adaptive Modulation and Coding (AMC) procedure. In practical systems such as the LTE the number of codewords is limited to nCW=2 because it represents a good trade-off between achievable performance and system complexity. After encoding and modulation the nCW codewords are mapped over the nlay≧nCW layers in the layer mapping block. The simplest mapping rule can be a one-to-one mapping in the case that the number of codeword is equal to the number of layers (i.e. nCW=nlay). In general, when the number of layers is larger that the number of codewords (i.e. nlay>nCW), the layer mapping block acts as a demultiplexer that maps one codeword over two or more layers.
The selection of the optimum precoding matrix is performed at the User Equipment (UE) as a function of the current CSI. The selection criteria implemented at the UE is not standardized and thus can be optimized by a given UE manufacturer in order to find the best trade-off between performance and complexity.
In case of MIMO-OFDM (Orthogonal Frequency Division Multiplexing) based systems, the PMI feedback must be provided for each subcarrier or at least for each group of adjacent subcarriers, due to the frequency selectivity of the channel. This means that the signalling overhead may become significant and, thus, several methods have been studied to reduce such feedback by exploiting, for instance, the correlation of the optimal precoding matrix over adjacent subcarriers.
One important aspect in the application of precoding in MIMO communication systems is the definition of a suitable selection function to be used at the receiver for the selection of the optimum precoding matrix as a function of the current CSI. In general, the selection function depends on the receiver type, on the characteristics of the precoding matrices that form the codebook and also on the metrics that are maximized or minimized by the function (e.g. Bit Error Rate—BER —, Signal to Noise Ratio—SNR —, minimum distance of the constellation at the receiver, capacity, practical rank, etc.).
In literature there are few examples of selection functions that can be used in case of unitary precoding. One exemplary function is provided in D. J. Love, R. W. Heath, Jr., “Limited Feedback Unitary Precoding for Spatial Multiplexing Systems”. IEEE Transactions On Information Theory, Vol. 51, No. 8, August 2005. Specifically, in this reference it is indicated that one possible precoding selection function S is the one that maximizes the SINR after spatial demultiplexing of the weakest layer in case of transmission of multiple layers (i.e. for nlay>1). In formulas this selection criterion can be expressed as follows:
            F              _        _              m    =            max              j        ∈                  {                      1            ,            2            ,            …            ,            M                    }                      ⁢          {              min        ⁡                  (                                    SNR              1                              (                j                )                                      ,                          SNR              2                              (                j                )                                      ,            …            ⁢                                                  ,                          SNR                              n                lay                                            (                j                )                                              )                    }      where the selection of the optimum precoding matrix Fm requires the computation of the SINR (Signal to Interference and Noise Ratio) of each of the nlay received layers. This computation involves the inversion of a complex matrix with size nlay×nlay that must be repeated for each matrix in the codebook (i.e. M times, if M is the number of precoding matrices belonging to the codebook) and for each subcarrier or group of adjacent subcarriers (i.e. NSC times if NSC is the number of used subcarriers). The inversion of such matrix involves a significant computation load at the user terminal especially when the number of transmitted layers is larger than 2 (i.e. nlay>2). In addition the mathematical expression of the SINR after spatial demultiplexing is available in case of linear receivers, such as MMSE (Minimum Mean Square Error) or ZF (Zero Forcing), but for other spatial demultiplexing algorithms it can be very difficult to determine a correspondent mathematical expression.
Another example of selection function is provided in WO 2006/023832 where it is described a method for providing closed loop transmit precoding by using a codebook formed of unitary matrices. Also in this case the selection of the precoding matrix is based on the weakest stream maximization where, of the P received streams, the smallest SINR value is maximized over the matrices in the codebook.
US 20080188190 describes a Multi-Rank BeamForming (MRBF) scheme in which the downlink channel is estimated and an optimal precoding matrix to be used by the MRBF transmitter is determined accordingly. The optimal precoding matrix is selected from a codebook of matrices having a recursive structure which allows for efficient computation of the optimal precoding matrix and corresponding SINR. The codebook also enjoys a small storage footprint. Due to the computational efficiency and modest memory requirements, the optimal precoding determination can be made at user equipment (UE) and communicated to a transmitting base station over a limited uplink channel for implementation over the downlink channel.
In general an adaptive MIMO system automatically switches from the spatial multiplexing to other MIMO techniques when the SINR and/or the practical rank decrease. An example of technique suitable for low SINR values is Space Time Coding (STC). However in real communication systems the adaptation procedure can be affected by errors and/or delays and therefore a selection function that is not optimal in the low SINR region may cause an undesired performance degradation.